Résumé : We discuss interval techniques for speeding up the exact evaluation of geometric predicates and describe an efficient implementation of interval arithmetic that is strongly influenced by the rounding modes of the widely used IEEE 754 standard. Using this approach we engineer an efficient floating point filter for the computation of the sign of a determinant that works for arbitrary dimensions. Furthermore we show how to use our interval techniques for exact linear optimization problems of low dimension as they arise in geometric computing. We validate our approach experimentally, comparing it with other static, dynamic and semi-static filters.